Fittings of the MB curves

To compare the differences between the three different samples in a more quan- titative manner, the MB curves were fitted with a single exponential:

∆n (t) = A exp (−t/τ ) , (7.1)

or:

ln (∆n (t)) = A − t/τ, (7.2) with A the offset in the MB at t = 0 and τ the decay constant of the MB signal. For the 16.5k samples, only the first 25 minutes were taken into account. For the 20.5k sample this range was limited to the first 6 minutes. For the 23k sample only the first 1.5 minutes were taken into account. The fits themselves are shown in the Appendix, section Figures 7.8 and 7.9. The results of the fits are shown in Table 7.2 and Figure 7.6. The measurements of the 16.5k sample performed at 20 T could not be fitted over the same time interval as the ones measured at 2 T (see Figure 7.9a,b), indicating that the alignment at 20 T becomes significantly different (out of the quadratic regime). This was not the case for the 20.5k sample. Most probably this is due to the fact that the 16.5k samples showed the largest aspect ratio’s and therefore have the largest magnetic anisotropy, leading to a saturation in the alignment at relative lower fields than is the case for the 20.5k and the 23k samples. For the 16.5k samples, the average decay time and its spread was therefore calculated using the 2 T measurements only, leading to an average value of τ of (14.2 ± 2.1) minutes. For the 20.5k samples, all measurements were taken into account since no deviations at 20 T in the alignment behavior were observed. The average value of τ was determined to be (3.6 ± 0.5) minutes. For the 23k, only the 20 T measurements were used since no values could be obtained at 2 T, as was explained before. For this sample, an average value for τ of (1.182 ± 0.010) minutes was obtained. These values all differ significantly and show that polymer length clearly influences the decay rate of the MB.

7.4

Discussion

The observation that shape changes in polymersomes can be induced just by transferring the sample from one container to the other might be the beginning of a whole new approach in controlling polymersome morphologies. For now,

7.4 Discussion

Sample measured at Figure fit

(Appendix) τ (min) average τ (min) 16.5k, batch 1 2 T 7.8a 12.8 14.2 ± 2.1 16.5k, batch 1 2 T 7.8b 13.7 16.5k, batch 1 2 T 7.8c 15.7 16.5k, batch 2 2 T 7.8d 16.8 16.5k, batch 2 2 T 7.8e 12.0 20.5k, batch 1 2 T 7.8f 3.2 3.6 ± 0.5 20.5k, batch 1 2 T 7.8g 3.7 20.5k, batch 1 2 T 7.8h 3.2 20.5k, batch 2 2 T 7.8i 4.5 20.5k, batch 2 2 T 7.8j 3.4 20.5k, batch 2 20 T 7.9c 3.7 20.5k, batch 2 20 T 7.9d 3.6 23k, batch 1 20 T 7.9e 1.175 1.182 ± 0.010 23k, batch 1 20 T 7.9f 1.880

Table 7.2: Results obtained from fitting the MB curves for all three samples. The final average result with error are given in the last column.

Figure 7.6: Experimentally determined recovery times (τ ) as function of the PS length. The red dashed line represents a linear fit.

7 Changing polymersome shapes by pipetting: rod formation and the...

the observed shape changes are limited to the formation of rods, but there might be combinations of solvent compositions and pipettes that could lead to other morphologies as well. Compared to dialysis and equilibration processes, this method has the advantage that it works very fast, usually within half a minute.

On the other hand, the results described in this chapter should also be considered as a warning. Often such effects are not expected and can then easily be missed or falsely assumed to be caused by any other effect. The data presented in this chapter clearly demonstrates that it is the pipetting itself which is causing the shape transformation from spheres into rods. It is striking that this shape transformation is only observed when using a glass Pasteur pipette. Until now, the reason for this is not clear. It is possible that the shape changes are caused by shear forces that arise during pipetting of the sample. The openings of the three tools also have different diameters, which could also influence the shear force when the sample is being taken in. It is very well possible that the material of the pipette is related. The glass Pasteur pipette is the only tool made out of glass, while the other two are of plastic and/or steel, which could also effect the shear force. The Pasteur pipette might also be the only tool which sucks up the solution the most violently, thereby creating a fast and strong pressure drop above the sample solution. This would then lead to a fast equilibration by evaporation of solvents, which in turn would lead to an osmotic pressure over the polymersome membrane. It is even possible that this leads the polymersomes membranes to burst or crack.

The polymersomes assembled from the largest polymers are affected the least when pipetting them with a glass Pasteur pipette (lowest MB, lowest aspect ratio). This is expected since longer polymers are expected to give the membrane a higher rigidity. The effect of polymer length on the relaxation time is unexpected however. The polymersomes assembled from the longest polymers recover the fastest after pipetting. This could be explained by the fact that the bending constant κ is highest for the polymersomes made from the longest polymersomes. Therefore the absolute change in the bending energy between spheres and rods increases when the polymer length increases. The larger change in energy might therefore be linked to faster kinetics and thus a shorter relaxation time. It might also be the case that polymersome membranes made from longer polymers might show more small cracks and imperfections, allowing water to flow through more easily. Diffusion studies, for instance by NMR, are necessary to determine if the observed differences in relaxation time are really caused by differences in diffusion rates.

So far, these shape changes have only been observed for polymersomes pre- pared in 1:1 water: organic solvent ratio’s, and only when transferring it with a

7.5 Conclusions

glass Pasteur pipette. In the research described in all previous chapters, these effects have not been observed since pipetting was either performed by plastic pipettes, or because samples were too rigid to be effected. The combination of electron microscopy and MB has proven to be a good set of tools to check for such effects.

7.5

Conclusions

Beside providing some interesting effects and a potential new method to make rods, the experiments in this chapter also pose a clear warning. It has become apparent that pipetting methods can change the morphology of polymersomes, depending on the solvent composition and the pipetting method. In this chapter we have shown that, using a glass Pasteur pipette, we can change the morphol- ogy of a polymersome sample from spheres to rods. The reason for this shape transformation is not yet clear, however, the effects are reproducible. Factors that need to be studied in more depth are the influence of the opening diameter of the glass pipettes and the speed at which the sample is being taken up by the pipette. The rod-shaped polymersomes were also observed to inflate back to their original spherical morphology. A clear dependence on polymer length was found, with the polymersomes assembled from the longest polymers being ones that inflate fastest. Diffusion studies over the membrane, by NMR for example, might provide new insights in the polymer length dependence on the inflation rate. For now, this study should be regarded as a critical overview of polymersome sample handling. We advise to always check for shape changes after transferring a polymersome sample from one container to another.

7 Changing polymersome shapes by pipetting: rod formation and the...

7.6

Appendix

Figure 7.7: (a) MB measurements on a 16.5k polymersome sample. The red dashed arrow represents the transfer of the sample into the cuvette by the glass Pasteur pipette, after which the MB was measured. (b) Corresponding TEM images of the sample quenched at different points in time as indicated in the MB curve. The first TEM image shows the sample before it is transferred into the cuvette (therefore not indicated in Figure (a)). The polymersomes all look spherical. The second image shows the sample right after pipetting it into the cuvette. Most polymersomes have adopted a rod-like morphology. The last TEM image is taken when the MB was back at zero. The image shows spherical polymersomes again, indicating that the rod-shaped polymersomes re-inflate over time to obtain their original spherical morphology. All scale bars are 500 nm.

7.6 Appendix

Figure 7.8: Single-exponential fits (red line) performed on the MB curves (blue line) for the 16.5k and 20.5k samples which were measured at 2 T. For the 16.5k samples, only the first 25 minutes of the curves are fitted since data points measured later become to noisy. For the 20.5k samples the first 6 minutes were fitted for the very same reasons. The results of the fits are given in Table 7.2.

7 Changing polymersome shapes by pipetting: rod formation and the...

Figure 7.9: Single-exponential fits (red line) performed on the MB curves (blue line) for the 16.5k, 20.5k and 23k samples which were measured at 20 T. For the 16.5k samples, the first 25 minutes of the curves are fitted since this was also done for the data obtained at 2 T. However, for the MB curves measured at 20 T we clearly see that the fits are not correct and that the decay is not single-exponential over this time interval. The results of the fittings of the 2 T and 20 T measurements can therefore not be compared. For the 20.5k samples the first 6 minutes were fitted as was the case for the 2 T measurements. For this sample, the decay is also mono-exponential at 20 T over the same time interval as the 2 T measurement. The 23k sample has been fitted over the first 1.5 minutes. No reference with 2 T measurements were possible since the signal to noise was too low too obtain a usable MB curve. However, based on the size of the MB, the aspect ratio of 23k rods will be even smaller than that of the 20.5k rods, and therefore the values obtained at 20 T would probably be similar to those at 2 T if they were measurable.

References

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Chapter 8

Towards dynamic light

scattering in high magnetic

fields

Abstract

In this chapter we describe the design and development of a new insert for measuring dual-angle dynamic light scattering in a Bitter magnet of the HFML. A design is presented based on the theoretical prediction that the anisotropic diffusion coefficients of an anisotrop- ically shaped particle can be determined by magnetically aligning these particles. A first version of the insert has been constructed and tested on a variety of differently shaped polymersomes, includ- ing spheres, discs and tubes. The setup is demonstrated to work up to 23.5 T, above which deviations are observed which are most probably caused by coupling of the insert itself to the strong mag- netic field. Up to 23.5 T, clear changes in the measured diffusion coefficients between the different samples are observed which are in accordance with theory for the higher scattering angles but not for the lower scattering angles. Suggestions for possible improvements are given to increase sensitivity and decrease magnetic interference.

8 Towards dynamic light scattering in high magnetic fields

8.1

Introduction

Over the last few decades, DLS has become a routine technique for particle characterization in the fields of soft matter and nanomaterials [1, 2]. In most cases polarized DLS is used, where only the light with an identical polarization as the incoming light is analyzed. This type of DLS provides translational diffusion coefficients, which can easily be translated to a hydrodynamic radius via the Stokes-Einstein relation [3, 4]. It is also possible to analyze only that light which is polarized perpendicular to the polarization of the incoming light. This configuration is called depolarized DLS, and is used to obtain rotational diffusion coefficients [5–9].

By measuring depolarized DLS in a magnetic field, one basically determines the degree of alignment, since full magnetic alignment will stop rotation along one axis altogether. However, the degree of alignment can already be accurately be measured with magnetic birefringence as was demonstrated in chapters 4, 5 and 6. Also, measuring depolarized DLS in a magnetic field is practically impossible because it is extremely sensitive to small changes in the polarization of the light [7]. In a magnetic field, the polarization will undoubtedly be altered to a certain extent because of Faraday rotation, making depolarized DLS in a magnetic field practically impossible. Polarized DLS however should be much easier to perform in a magnetic field, since it is much less sensitive to small changes in polarization. Also, polarized DLS provides translational diffusion coefficients which can be related to linear translational motion. Since linear motion cannot be measured with magnetic birefringence, it is therefore a useful complementary technique.

So far, DLS measurements in high magnetic fields are scarce. The ability to measure DLS in high magnetic fields would be beneficial for two reasons. First of all, it provides the possibility to determine the size of nanoparticles in high magnetic fields. Phenomena like aggregation and self-assembly can then be studied in situ. Also the work on magnetically induced growth of lipid vesi- cles, as reported by Ozeki [10], might benefit from in situ DLS. Second of all, it may even be possible to measure magnetic alignment on anisotropically shaped particles by measuring the diffusion coefficients parallel and perpendicular to the magnetic field. Research in the field of soft matter in high magnetic fields would benefit greatly from such a technique. Also with respect to the investi- gation of polymersomes, DLS in magnetic fields could significantly add to the understanding of motion of polymersomes in a magnetic field, since it is the translational diffusion coefficient that is being measured [11].

Measuring (polarized) DLS at high magnetic fields has been reported once before by Challa et al. [12]. They reported the investigation of liquid crystal